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Simplifying 5x + x2 = 2532 Solving 5x + x2 = 2532 Solving for variable 'x'. Reorder the terms: -2532 + 5x + x2 = 2532 + -2532 Combine like terms: 2532 + -2532 = 0 -2532 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2532' to each side of the equation. -2532 + 5x + 2532 + x2 = 0 + 2532 Reorder the terms: -2532 + 2532 + 5x + x2 = 0 + 2532 Combine like terms: -2532 + 2532 = 0 0 + 5x + x2 = 0 + 2532 5x + x2 = 0 + 2532 Combine like terms: 0 + 2532 = 2532 5x + x2 = 2532 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2532 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2532 + 6.25 Combine like terms: 2532 + 6.25 = 2538.25 6.25 + 5x + x2 = 2538.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2538.25 Calculate the square root of the right side: 50.381048024 Break this problem into two subproblems by setting (x + 2.5) equal to 50.381048024 and -50.381048024.Subproblem 1
x + 2.5 = 50.381048024 Simplifying x + 2.5 = 50.381048024 Reorder the terms: 2.5 + x = 50.381048024 Solving 2.5 + x = 50.381048024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 50.381048024 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 50.381048024 + -2.5 x = 50.381048024 + -2.5 Combine like terms: 50.381048024 + -2.5 = 47.881048024 x = 47.881048024 Simplifying x = 47.881048024Subproblem 2
x + 2.5 = -50.381048024 Simplifying x + 2.5 = -50.381048024 Reorder the terms: 2.5 + x = -50.381048024 Solving 2.5 + x = -50.381048024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -50.381048024 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -50.381048024 + -2.5 x = -50.381048024 + -2.5 Combine like terms: -50.381048024 + -2.5 = -52.881048024 x = -52.881048024 Simplifying x = -52.881048024Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.881048024, -52.881048024}
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